An architect makes a scale drawing of a house. In real life, the width of the porch is 7 meters. On the drawing, the width is 4 cm. What scale was used for the drawing?

7 meters : 4 cm = 700 cm: 4 cm (1 meter is 100 centimeters)

175 cm: 1 cm (divide both sides of the proportion by 4)

The scale drawing is 1/175 of the real life porch

Scale is 1/175

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.